

A348776


The numbers >= 2 with 3 repeated.


1



2, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83
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OFFSET

1,1


COMMENTS

This sequence, 2, 3, 3, 4, 5, 6, 7, ..., gives the stable range of the polynomial rings Z, Z[x_1], Z[x_1, x_2], Z[x_1, x_2, x_3], ...
A note on terminology: "stable range" and "stable rank" are the same thing. In the Englishspeaking world, people have always used the term "stable range", which was what Bass had invented in the early '60s. When Russian workers wrote on this theme, of course they used a Russian translation of the term "stable range". When the term was translated back into English, it became "stable rank"!  T. Y. Lam, Nov 07 2021


REFERENCES

T. Y. Lam, Excursions in Ring Theory, in preparation, 2021. See Section 24.


LINKS



FORMULA

a(n) = n for n >= 3.
a(n) = 2*a(n1)  a(n2) for n > 4.
G.f.: x*(x^3  x^2  x + 2)/(x  1)^2. (End)


PROG

(Python)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Nov 07 2021, following a suggestion from L. Guyot and T. Y. Lam.


STATUS

approved



